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More Sophistication
Usually don't know N in advance, so iterate to a desired accuracy: qtrap().
Higher-order method by cleverly adding refinements to cancel error terms: qsimp().
Generalization to order 2k (Richardson's deferred approach to the limit): qromb().
For improper integrals, generally need open formulae (not evaluated at endpoints).
For multi-D, use nested 1-D techniques.
Notes: